If I wanted to reach out to the owner, one could just open the phone app on the already unlocked phone and call anyone that seems like a close relative. Hoping for the owner to just randomly stumble into an internet post seems very impractical, considering that the phone likely contains a substantial amount of info about the owner.

Besides, why would the NTSB hold onto the phone for years? It's not part of the aircraft, there's no real reason why they'd need to have it at all. Is it just common with US government agencies?

Just call "Mum" and be done

The NTSB was already there before they posted the picture on twitter. They were posting it for the attention, not to give the phone back.